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<div class="title">SparseQR.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2012-2013 Desire Nuentsa &lt;desire.nuentsa_wakam@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2012-2014 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_SPARSE_QR_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_SPARSE_QR_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OrderingType&gt; <span class="keyword">class </span>SparseQR;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SparseQRType&gt; <span class="keyword">struct </span>SparseQRMatrixQReturnType;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SparseQRType&gt; <span class="keyword">struct </span>SparseQRMatrixQTransposeReturnType;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SparseQRType, <span class="keyword">typename</span> Derived&gt; <span class="keyword">struct </span>SparseQR_QProduct;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SparseQRType&gt; <span class="keyword">struct </span>traits&lt;SparseQRMatrixQReturnType&lt;SparseQRType&gt; &gt;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  {</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::MatrixType ReturnType;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> ReturnType::StorageIndex StorageIndex;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> ReturnType::StorageKind StorageKind;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;      RowsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>,</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;      ColsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    };</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  };</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SparseQRType&gt; <span class="keyword">struct </span>traits&lt;SparseQRMatrixQTransposeReturnType&lt;SparseQRType&gt; &gt;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  {</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::MatrixType ReturnType;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  };</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SparseQRType, <span class="keyword">typename</span> Derived&gt; <span class="keyword">struct </span>traits&lt;SparseQR_QProduct&lt;SparseQRType, Derived&gt; &gt;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  {</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  };</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;} <span class="comment">// End namespace internal</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160; </div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_, <span class="keyword">typename</span> OrderingType_&gt;</div>
<div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html">   86</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1SparseQR.html">SparseQR</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SparseSolverBase.html">SparseSolverBase</a>&lt;SparseQR&lt;MatrixType_,OrderingType_&gt; &gt;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;{</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseSolverBase.html">SparseSolverBase&lt;SparseQR&lt;MatrixType_,OrderingType_&gt;</a> &gt; <a class="code" href="classEigen_1_1SparseSolverBase.html">Base</a>;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    <span class="keyword">using</span> Base::_solve_impl;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keyword">typedef</span> OrderingType_ OrderingType;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::StorageIndex StorageIndex;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix&lt;Scalar,ColMajor,StorageIndex&gt;</a> <a class="code" href="classEigen_1_1SparseMatrix.html">QRMatrixType</a>;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;StorageIndex, Dynamic, 1&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">IndexVector</a>;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar, Dynamic, 1&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">ScalarVector</a>;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix&lt;Dynamic, Dynamic, StorageIndex&gt;</a> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>;</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;      ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    };</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    </div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <a class="code" href="classEigen_1_1SparseQR.html">SparseQR</a> () :  m_analysisIsok(<span class="keyword">false</span>), m_lastError(<span class="stringliteral">&quot;&quot;</span>), m_useDefaultThreshold(<span class="keyword">true</span>),m_isQSorted(<span class="keyword">false</span>),m_isEtreeOk(<span class="keyword">false</span>)</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    { }</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    </div>
<div class="line"><a name="l00118"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a5f13e65437ada7e10a85de8cd55db11d">  118</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1SparseQR.html#a5f13e65437ada7e10a85de8cd55db11d">SparseQR</a>(<span class="keyword">const</span> MatrixType&amp; mat) : m_analysisIsok(false), m_lastError(<span class="stringliteral">&quot;&quot;</span>), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    {</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;      <a class="code" href="classEigen_1_1SparseQR.html#aba8ae81fd3d4ce9139eccb6b7a0256b2">compute</a>(mat);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    }</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    </div>
<div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#aba8ae81fd3d4ce9139eccb6b7a0256b2">  129</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#aba8ae81fd3d4ce9139eccb6b7a0256b2">compute</a>(<span class="keyword">const</span> MatrixType&amp; mat)</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    {</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;      <a class="code" href="classEigen_1_1SparseQR.html#a4b425ddb1358c914d764cde48853a4f6">analyzePattern</a>(mat);</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;      <a class="code" href="classEigen_1_1SparseQR.html#a55a34bacf05bd30a1dacbccad9f03c6d">factorize</a>(mat);</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    }</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#a4b425ddb1358c914d764cde48853a4f6">analyzePattern</a>(<span class="keyword">const</span> MatrixType&amp; mat);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#a55a34bacf05bd30a1dacbccad9f03c6d">factorize</a>(<span class="keyword">const</span> MatrixType&amp; mat);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    </div>
<div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a9b196c075fdf32737b6843a615e79ea6">  139</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1SparseQR.html#a9b196c075fdf32737b6843a615e79ea6">rows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_pmat.<a class="code" href="classEigen_1_1SparseMatrix.html#a853a76dd42349fa2f3654a4a61e0f574">rows</a>(); }</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    </div>
<div class="line"><a name="l00143"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a6fdb992f3381ecc5b0a21a692fc0e0a4">  143</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1SparseQR.html#a6fdb992f3381ecc5b0a21a692fc0e0a4">cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_pmat.<a class="code" href="classEigen_1_1SparseMatrix.html#a36b8cc95234b4e2de38a199b6b2af9fc">cols</a>();}</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    </div>
<div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a7764a1f00c0d83f6423f81a4a40d5f8c">  158</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1SparseMatrix.html">QRMatrixType</a>&amp; <a class="code" href="classEigen_1_1SparseQR.html#a7764a1f00c0d83f6423f81a4a40d5f8c">matrixR</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_R; }</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    </div>
<div class="line"><a name="l00164"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">  164</a></span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">rank</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;The factorization should be called first, use compute()&quot;</span>);</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;      <span class="keywordflow">return</span> m_nonzeropivots; </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    }</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    </div>
<div class="line"><a name="l00188"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#aa3c7967f81ef047891a549a514908cd3">  188</a></span>&#160;    SparseQRMatrixQReturnType&lt;SparseQR&gt; <a class="code" href="classEigen_1_1SparseQR.html#aa3c7967f81ef047891a549a514908cd3">matrixQ</a>()<span class="keyword"> const </span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="keyword">    </span>{ <span class="keywordflow">return</span> SparseQRMatrixQReturnType&lt;SparseQR&gt;(*<span class="keyword">this</span>); }</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    </div>
<div class="line"><a name="l00194"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#aa27f024fe063684754047c531ab84a2b">  194</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>&amp; <a class="code" href="classEigen_1_1SparseQR.html#aa27f024fe063684754047c531ab84a2b">colsPermutation</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="keyword">    </span>{ </div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;Decomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;      <span class="keywordflow">return</span> m_outputPerm_c;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    }</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    </div>
<div class="line"><a name="l00203"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#ab9cc9c9d14e8c2f7587ca3f747bd1c14">  203</a></span>&#160;    std::string <a class="code" href="classEigen_1_1SparseQR.html#ab9cc9c9d14e8c2f7587ca3f747bd1c14">lastErrorMessage</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_lastError; }</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    </div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest&gt;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    <span class="keywordtype">bool</span> _solve_impl(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a> &amp;B, <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Dest&gt;</a> &amp;dest)<span class="keyword"> const</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;The factorization should be called first, use compute()&quot;</span>);</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;      eigen_assert(this-&gt;<a class="code" href="classEigen_1_1SparseQR.html#a9b196c075fdf32737b6843a615e79ea6">rows</a>() == B.<a class="code" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>() &amp;&amp; <span class="stringliteral">&quot;SparseQR::solve() : invalid number of rows in the right hand side matrix&quot;</span>);</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160; </div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">rank</a> = this-&gt;<a class="code" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">rank</a>();</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;      </div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;      <span class="comment">// Compute Q^* * b;</span></div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;      <span class="keyword">typename</span> Dest::PlainObject y, b;</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;      y = this-&gt;<a class="code" href="classEigen_1_1SparseQR.html#aa3c7967f81ef047891a549a514908cd3">matrixQ</a>().adjoint() * B;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;      b = y;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;      </div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;      <span class="comment">// Solve with the triangular matrix R</span></div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;      y.resize((std::max&lt;Index&gt;)(<a class="code" href="classEigen_1_1SparseQR.html#a6fdb992f3381ecc5b0a21a692fc0e0a4">cols</a>(),y.rows()),y.cols());</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;      y.topRows(<a class="code" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">rank</a>) = this-&gt;<a class="code" href="classEigen_1_1SparseQR.html#a7764a1f00c0d83f6423f81a4a40d5f8c">matrixR</a>().topLeftCorner(rank, <a class="code" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">rank</a>).template triangularView&lt;Upper&gt;().solve(b.topRows(<a class="code" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">rank</a>));</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;      y.bottomRows(y.rows()-<a class="code" href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">rank</a>).setZero();</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;      </div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;      <span class="comment">// Apply the column permutation</span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;      <span class="keywordflow">if</span> (m_perm_c.<a class="code" href="classEigen_1_1PermutationBase.html#a2216f9ce7b453ac39c46ff0323daeac9">size</a>())  dest = <a class="code" href="classEigen_1_1SparseQR.html#aa27f024fe063684754047c531ab84a2b">colsPermutation</a>() * y.topRows(<a class="code" href="classEigen_1_1SparseQR.html#a6fdb992f3381ecc5b0a21a692fc0e0a4">cols</a>());</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;      <span class="keywordflow">else</span>                  dest = y.topRows(<a class="code" href="classEigen_1_1SparseQR.html#a6fdb992f3381ecc5b0a21a692fc0e0a4">cols</a>());</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;      </div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;      m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    }</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a05f11a211307cb106e9e47ee9730d7ed">  237</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#a05f11a211307cb106e9e47ee9730d7ed">setPivotThreshold</a>(<span class="keyword">const</span> RealScalar&amp; threshold)</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    {</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      m_useDefaultThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;      m_threshold = threshold;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    }</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    </div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00248"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#aa77f5cb833bbea615adb532139761971">  248</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;SparseQR, Rhs&gt;</a> <a class="code" href="classEigen_1_1SparseQR.html#aa77f5cb833bbea615adb532139761971">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a>&amp; B)<span class="keyword"> const </span></div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;The factorization should be called first, use compute()&quot;</span>);</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;      eigen_assert(this-&gt;<a class="code" href="classEigen_1_1SparseQR.html#a9b196c075fdf32737b6843a615e79ea6">rows</a>() == B.<a class="code" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>() &amp;&amp; <span class="stringliteral">&quot;SparseQR::solve() : invalid number of rows in the right hand side matrix&quot;</span>);</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;SparseQR, Rhs&gt;</a>(*<span class="keyword">this</span>, B.<a class="code" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>());</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    }</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;SparseQR, Rhs&gt;</a> <a class="code" href="classEigen_1_1SparseQR.html#aa77f5cb833bbea615adb532139761971">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1SparseMatrixBase.html">SparseMatrixBase&lt;Rhs&gt;</a>&amp; B)<span class="keyword"> const</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;          eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;The factorization should be called first, use compute()&quot;</span>);</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;          eigen_assert(this-&gt;<a class="code" href="classEigen_1_1SparseQR.html#a9b196c075fdf32737b6843a615e79ea6">rows</a>() == B.<a class="code" href="classEigen_1_1SparseMatrixBase.html#a1944e9fa9ce7937bfc3a87b2cb94371f">rows</a>() &amp;&amp; <span class="stringliteral">&quot;SparseQR::solve() : invalid number of rows in the right hand side matrix&quot;</span>);</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;          <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;SparseQR, Rhs&gt;</a>(*<span class="keyword">this</span>, B.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>());</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    }</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;    </div>
<div class="line"><a name="l00270"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#ae9da700b8c3b9bb30ff77508c359e764">  270</a></span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code" href="classEigen_1_1SparseQR.html#ae9da700b8c3b9bb30ff77508c359e764">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;Decomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;      <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    }</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160; </div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> _sort_matrix_Q()</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    {</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;      <span class="keywordflow">if</span>(this-&gt;m_isQSorted) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;      <span class="comment">// The matrix Q is sorted during the transposition</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;      <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix&lt;Scalar, RowMajor, Index&gt;</a> mQrm(this-&gt;m_Q);</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;      this-&gt;m_Q = mQrm;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;      this-&gt;m_isQSorted = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;    }</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160; </div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    </div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    <span class="keywordtype">bool</span> m_analysisIsok;</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    <span class="keywordtype">bool</span> m_factorizationIsok;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    <span class="keyword">mutable</span> <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    std::string m_lastError;</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    QRMatrixType m_pmat;            <span class="comment">// Temporary matrix</span></div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    QRMatrixType m_R;               <span class="comment">// The triangular factor matrix</span></div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    QRMatrixType m_Q;               <span class="comment">// The orthogonal reflectors</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;    ScalarVector m_hcoeffs;         <span class="comment">// The Householder coefficients</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    PermutationType m_perm_c;       <span class="comment">// Fill-reducing  Column  permutation</span></div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    PermutationType m_pivotperm;    <span class="comment">// The permutation for rank revealing</span></div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    PermutationType m_outputPerm_c; <span class="comment">// The final column permutation</span></div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;    RealScalar m_threshold;         <span class="comment">// Threshold to determine null Householder reflections</span></div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;    <span class="keywordtype">bool</span> m_useDefaultThreshold;     <span class="comment">// Use default threshold</span></div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m_nonzeropivots;          <span class="comment">// Number of non zero pivots found</span></div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    IndexVector m_etree;            <span class="comment">// Column elimination tree</span></div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;    IndexVector m_firstRowElt;      <span class="comment">// First element in each row</span></div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    <span class="keywordtype">bool</span> m_isQSorted;               <span class="comment">// whether Q is sorted or not</span></div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    <span class="keywordtype">bool</span> m_isEtreeOk;               <span class="comment">// whether the elimination tree match the initial input matrix</span></div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    </div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span>, <span class="keyword">typename</span> &gt; <span class="keyword">friend</span> <span class="keyword">struct </span>SparseQR_QProduct;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    </div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;};</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160; </div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OrderingType&gt;</div>
<div class="line"><a name="l00322"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a4b425ddb1358c914d764cde48853a4f6">  322</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#a4b425ddb1358c914d764cde48853a4f6">SparseQR&lt;MatrixType,OrderingType&gt;::analyzePattern</a>(<span class="keyword">const</span> MatrixType&amp; mat)</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;{</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  eigen_assert(mat.isCompressed() &amp;&amp; <span class="stringliteral">&quot;SparseQR requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to SparseQR&quot;</span>);</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;  <span class="comment">// Copy to a column major matrix if the input is rowmajor</span></div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  std::conditional_t&lt;MatrixType::IsRowMajor,QRMatrixType,const MatrixType&amp;&gt; matCpy(mat);</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;  <span class="comment">// Compute the column fill reducing ordering</span></div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  OrderingType ord; </div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  ord(matCpy, m_perm_c); </div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = mat.cols();</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = mat.rows();</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> diagSize = (std::min)(m,n);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  </div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  <span class="keywordflow">if</span> (!m_perm_c.size())</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  {</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    m_perm_c.resize(n);</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;    m_perm_c.indices().setLinSpaced(n, 0,StorageIndex(n-1));</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  }</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  </div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  <span class="comment">// Compute the column elimination tree of the permuted matrix</span></div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  m_outputPerm_c = m_perm_c.inverse();</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  internal::coletree(matCpy, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  m_isEtreeOk = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  </div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  m_R.resize(m, n);</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;  m_Q.resize(m, diagSize);</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  </div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  <span class="comment">// Allocate space for nonzero elements: rough estimation</span></div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;  m_R.reserve(2*mat.nonZeros()); <span class="comment">//FIXME Get a more accurate estimation through symbolic factorization with the etree</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  m_Q.reserve(2*mat.nonZeros());</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  m_hcoeffs.resize(diagSize);</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  m_analysisIsok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;}</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160; </div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OrderingType&gt;</div>
<div class="line"><a name="l00363"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a55a34bacf05bd30a1dacbccad9f03c6d">  363</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#a55a34bacf05bd30a1dacbccad9f03c6d">SparseQR&lt;MatrixType,OrderingType&gt;::factorize</a>(<span class="keyword">const</span> MatrixType&amp; mat)</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;{</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  </div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  eigen_assert(m_analysisIsok &amp;&amp; <span class="stringliteral">&quot;analyzePattern() should be called before this step&quot;</span>);</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  StorageIndex m = StorageIndex(mat.rows());</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  StorageIndex n = StorageIndex(mat.cols());</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;  StorageIndex diagSize = (std::min)(m,n);</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  <a class="code" href="classEigen_1_1Matrix.html">IndexVector</a> mark((std::max)(m,n)); mark.<a class="code" href="classEigen_1_1PlainObjectBase.html#aac6bc5261783ec3008a51c2654de73e8">setConstant</a>(-1);  <span class="comment">// Record the visited nodes</span></div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  <a class="code" href="classEigen_1_1Matrix.html">IndexVector</a> Ridx(n), Qidx(m);                             <span class="comment">// Store temporarily the row indexes for the current column of R and Q</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nzcolR, nzcolQ;                                     <span class="comment">// Number of nonzero for the current column of R and Q</span></div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  <a class="code" href="classEigen_1_1Matrix.html">ScalarVector</a> tval(m);                                     <span class="comment">// The dense vector used to compute the current column</span></div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  RealScalar pivotThreshold = m_threshold;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  </div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;  m_R.setZero();</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  m_Q.setZero();</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  m_pmat = mat;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;  <span class="keywordflow">if</span>(!m_isEtreeOk)</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;  {</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    m_outputPerm_c = m_perm_c.inverse();</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    internal::coletree(m_pmat, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    m_isEtreeOk = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  }</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160; </div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  m_pmat.uncompress(); <span class="comment">// To have the innerNonZeroPtr allocated</span></div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;  </div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;  <span class="comment">// Apply the fill-in reducing permutation lazily:</span></div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  {</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    <span class="comment">// If the input is row major, copy the original column indices,</span></div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    <span class="comment">// otherwise directly use the input matrix</span></div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    <span class="comment">// </span></div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    <a class="code" href="classEigen_1_1Matrix.html">IndexVector</a> originalOuterIndicesCpy;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    <span class="keyword">const</span> StorageIndex *originalOuterIndices = mat.outerIndexPtr();</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    <span class="keywordflow">if</span>(MatrixType::IsRowMajor)</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    {</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;      originalOuterIndicesCpy = IndexVector::Map(m_pmat.outerIndexPtr(),n+1);</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;      originalOuterIndices = originalOuterIndicesCpy.<a class="code" href="classEigen_1_1PlainObjectBase.html#ac54123f62de4c46a9107ff53890b6116">data</a>();</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    }</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    </div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++)</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    {</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = m_perm_c.size() ? m_perm_c.indices()(i) : i;</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;      m_pmat.outerIndexPtr()[p] = originalOuterIndices[i]; </div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;      m_pmat.innerNonZeroPtr()[p] = originalOuterIndices[i+1] - originalOuterIndices[i]; </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    }</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;  }</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;  </div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;  <span class="comment">/* Compute the default threshold as in MatLab, see:</span></div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="comment">   * Tim Davis, &quot;Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing</span></div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<span class="comment">   * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 </span></div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;<span class="comment">   */</span></div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;  <span class="keywordflow">if</span>(m_useDefaultThreshold) </div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;  {</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    RealScalar max2Norm = 0.0;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) max2Norm = numext::maxi(max2Norm, m_pmat.col(j).norm());</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keywordflow">if</span>(max2Norm==RealScalar(0))</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;      max2Norm = RealScalar(1);</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;    pivotThreshold = 20 * (m + n) * max2Norm * <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;RealScalar&gt;::epsilon</a>();</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  }</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  </div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;  <span class="comment">// Initialize the numerical permutation</span></div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  m_pivotperm.setIdentity(n);</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;  </div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;  StorageIndex nonzeroCol = 0; <span class="comment">// Record the number of valid pivots</span></div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  m_Q.startVec(0);</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160; </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;  <span class="comment">// Left looking rank-revealing QR factorization: compute a column of R and Q at a time</span></div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;  <span class="keywordflow">for</span> (StorageIndex col = 0; col &lt; n; ++col)</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;  {</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    mark.<a class="code" href="classEigen_1_1PlainObjectBase.html#aac6bc5261783ec3008a51c2654de73e8">setConstant</a>(-1);</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    m_R.startVec(col);</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;    mark(nonzeroCol) = col;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    Qidx(0) = nonzeroCol;</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;    nzcolR = 0; nzcolQ = 1;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;    <span class="keywordtype">bool</span> found_diag = nonzeroCol&gt;=m;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    tval.<a class="code" href="classEigen_1_1PlainObjectBase.html#acc39eaf7ba22b725c86f1b9b8bb57c3c">setZero</a>(); </div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    </div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="comment">// Symbolic factorization: find the nonzero locations of the column k of the factors R and Q, i.e.,</span></div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    <span class="comment">// all the nodes (with indexes lower than rank) reachable through the column elimination tree (etree) rooted at node k.</span></div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <span class="comment">// Note: if the diagonal entry does not exist, then its contribution must be explicitly added,</span></div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <span class="comment">// thus the trick with found_diag that permits to do one more iteration on the diagonal element if this one has not been found.</span></div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    <span class="keywordflow">for</span> (<span class="keyword">typename</span> QRMatrixType::InnerIterator itp(m_pmat, col); itp || !found_diag; ++itp)</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    {</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;      StorageIndex curIdx = nonzeroCol;</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;      <span class="keywordflow">if</span>(itp) curIdx = StorageIndex(itp.row());</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;      <span class="keywordflow">if</span>(curIdx == nonzeroCol) found_diag = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;      </div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;      <span class="comment">// Get the nonzeros indexes of the current column of R</span></div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;      StorageIndex st = m_firstRowElt(curIdx); <span class="comment">// The traversal of the etree starts here</span></div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;      <span class="keywordflow">if</span> (st &lt; 0 )</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;      {</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;        m_lastError = <span class="stringliteral">&quot;Empty row found during numerical factorization&quot;</span>;</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;        m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf">InvalidInput</a>;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;        <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;      }</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160; </div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;      <span class="comment">// Traverse the etree </span></div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> bi = nzcolR;</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;      <span class="keywordflow">for</span> (; mark(st) != col; st = m_etree(st))</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;      {</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;        Ridx(nzcolR) = st;  <span class="comment">// Add this row to the list,</span></div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;        mark(st) = col;     <span class="comment">// and mark this row as visited</span></div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;        nzcolR++;</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;      }</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160; </div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;      <span class="comment">// Reverse the list to get the topological ordering</span></div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nt = nzcolR-bi;</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; nt/2; i++) std::swap(Ridx(bi+i), Ridx(nzcolR-i-1));</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;       </div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;      <span class="comment">// Copy the current (curIdx,pcol) value of the input matrix</span></div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;      <span class="keywordflow">if</span>(itp) tval(curIdx) = itp.value();</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;      <span class="keywordflow">else</span>    tval(curIdx) = Scalar(0);</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;      </div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;      <span class="comment">// Compute the pattern of Q(:,k)</span></div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;      <span class="keywordflow">if</span>(curIdx &gt; nonzeroCol &amp;&amp; mark(curIdx) != col ) </div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;      {</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;        Qidx(nzcolQ) = curIdx;  <span class="comment">// Add this row to the pattern of Q,</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;        mark(curIdx) = col;     <span class="comment">// and mark it as visited</span></div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;        nzcolQ++;</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;      }</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;    }</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160; </div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;    <span class="comment">// Browse all the indexes of R(:,col) in reverse order</span></div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = nzcolR-1; i &gt;= 0; i--)</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;    {</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> curIdx = Ridx(i);</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;      </div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;      <span class="comment">// Apply the curIdx-th householder vector to the current column (temporarily stored into tval)</span></div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;      Scalar tdot(0);</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;      </div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;      <span class="comment">// First compute q&#39; * tval</span></div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;      tdot = m_Q.col(curIdx).dot(tval);</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160; </div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;      tdot *= m_hcoeffs(curIdx);</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;      </div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;      <span class="comment">// Then update tval = tval - q * tau</span></div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;      <span class="comment">// FIXME: tval -= tdot * m_Q.col(curIdx) should amount to the same (need to check/add support for efficient &quot;dense ?= sparse&quot;)</span></div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;      <span class="keywordflow">for</span> (<span class="keyword">typename</span> QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;        tval(itq.row()) -= itq.value() * tdot;</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160; </div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;      <span class="comment">// Detect fill-in for the current column of Q</span></div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;      <span class="keywordflow">if</span>(m_etree(Ridx(i)) == nonzeroCol)</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;      {</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;        <span class="keywordflow">for</span> (<span class="keyword">typename</span> QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;        {</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;          StorageIndex iQ = StorageIndex(itq.row());</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;          <span class="keywordflow">if</span> (mark(iQ) != col)</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;          {</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;            Qidx(nzcolQ++) = iQ;  <span class="comment">// Add this row to the pattern of Q,</span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;            mark(iQ) = col;       <span class="comment">// and mark it as visited</span></div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;          }</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;        }</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;      }</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;    } <span class="comment">// End update current column</span></div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;    </div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;    Scalar tau = RealScalar(0);</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;    RealScalar beta = 0;</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;    </div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;    <span class="keywordflow">if</span>(nonzeroCol &lt; diagSize)</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;    {</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;      <span class="comment">// Compute the Householder reflection that eliminate the current column</span></div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;      <span class="comment">// FIXME this step should call the Householder module.</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;      Scalar c0 = nzcolQ ? tval(Qidx(0)) : Scalar(0);</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;      </div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;      <span class="comment">// First, the squared norm of Q((col+1):m, col)</span></div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;      RealScalar sqrNorm = 0.;</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> itq = 1; itq &lt; nzcolQ; ++itq) sqrNorm += numext::abs2(tval(Qidx(itq)));</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;      <span class="keywordflow">if</span>(sqrNorm == RealScalar(0) &amp;&amp; numext::imag(c0) == RealScalar(0))</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;      {</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;        beta = numext::real(c0);</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;        tval(Qidx(0)) = 1;</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;      }</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;      {</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;        <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;        beta = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(numext::abs2(c0) + sqrNorm);</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;        <span class="keywordflow">if</span>(numext::real(c0) &gt;= RealScalar(0))</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;          beta = -beta;</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;        tval(Qidx(0)) = 1;</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;        <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> itq = 1; itq &lt; nzcolQ; ++itq)</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;          tval(Qidx(itq)) /= (c0 - beta);</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;        tau = numext::conj((beta-c0) / beta);</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;          </div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;      }</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    }</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160; </div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    <span class="comment">// Insert values in R</span></div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>  i = nzcolR-1; i &gt;= 0; i--)</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;    {</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> curIdx = Ridx(i);</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;      <span class="keywordflow">if</span>(curIdx &lt; nonzeroCol) </div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;      {</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;        m_R.insertBackByOuterInnerUnordered(col, curIdx) = tval(curIdx);</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;        tval(curIdx) = Scalar(0.);</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;      }</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;    }</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160; </div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;    <span class="keywordflow">if</span>(nonzeroCol &lt; diagSize &amp;&amp; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(beta) &gt;= pivotThreshold)</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;    {</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;      m_R.insertBackByOuterInner(col, nonzeroCol) = beta;</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;      <span class="comment">// The householder coefficient</span></div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;      m_hcoeffs(nonzeroCol) = tau;</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;      <span class="comment">// Record the householder reflections</span></div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> itq = 0; itq &lt; nzcolQ; ++itq)</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;      {</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> iQ = Qidx(itq);</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;        m_Q.insertBackByOuterInnerUnordered(nonzeroCol,iQ) = tval(iQ);</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;        tval(iQ) = Scalar(0.);</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;      }</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;      nonzeroCol++;</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;      <span class="keywordflow">if</span>(nonzeroCol&lt;diagSize)</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;        m_Q.startVec(nonzeroCol);</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;    }</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;    {</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;      <span class="comment">// Zero pivot found: move implicitly this column to the end</span></div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;      <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = nonzeroCol; j &lt; n-1; j++) </div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;        std::swap(m_pivotperm.indices()(j), m_pivotperm.indices()[j+1]);</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;      </div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;      <span class="comment">// Recompute the column elimination tree</span></div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;      internal::coletree(m_pmat, m_etree, m_firstRowElt, m_pivotperm.indices().data());</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;      m_isEtreeOk = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;    }</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;  }</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;  </div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;  m_hcoeffs.tail(diagSize-nonzeroCol).setZero();</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  </div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  <span class="comment">// Finalize the column pointers of the sparse matrices R and Q</span></div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;  m_Q.finalize();</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  m_Q.makeCompressed();</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  m_R.finalize();</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;  m_R.makeCompressed();</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;  m_isQSorted = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160; </div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;  m_nonzeropivots = nonzeroCol;</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;  </div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;  <span class="keywordflow">if</span>(nonzeroCol&lt;n)</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;  {</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;    <span class="comment">// Permute the triangular factor to put the &#39;dead&#39; columns to the end</span></div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;    <a class="code" href="classEigen_1_1SparseMatrix.html">QRMatrixType</a> tempR(m_R);</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;    m_R = tempR * m_pivotperm;</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;    </div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;    <span class="comment">// Update the column permutation</span></div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;    m_outputPerm_c = m_outputPerm_c * m_pivotperm;</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;  }</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;  </div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;  m_isInitialized = <span class="keyword">true</span>; </div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;  m_factorizationIsok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;  m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;}</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160; </div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> SparseQRType, <span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;<span class="keyword">struct </span>SparseQR_QProduct : ReturnByValue&lt;SparseQR_QProduct&lt;SparseQRType, Derived&gt; &gt;</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;{</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::QRMatrixType MatrixType;</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::Scalar Scalar;</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;  <span class="comment">// Get the references </span></div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;  SparseQR_QProduct(<span class="keyword">const</span> SparseQRType&amp; qr, <span class="keyword">const</span> Derived&amp; other, <span class="keywordtype">bool</span> transpose) : </div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;  m_qr(qr),m_other(other),m_transpose(transpose) {}</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;  <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.matrixQ().rows(); }</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;  <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_other.cols(); }</div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;  </div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;  <span class="comment">// Assign to a vector</span></div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> DesType&gt;</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  <span class="keywordtype">void</span> evalTo(DesType&amp; res)<span class="keyword"> const</span></div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = m_qr.rows();</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = m_qr.cols();</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> diagSize = (std::min)(m,n);</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;    res = m_other;</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;    <span class="keywordflow">if</span> (m_transpose)</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;    {</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;      eigen_assert(m_qr.m_Q.rows() == m_other.rows() &amp;&amp; <span class="stringliteral">&quot;Non conforming object sizes&quot;</span>);</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;      <span class="comment">//Compute res = Q&#39; * other column by column</span></div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; res.cols(); j++){</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;        <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; diagSize; k++)</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;        {</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;          Scalar tau = Scalar(0);</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;          tau = m_qr.m_Q.col(k).dot(res.col(j));</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;          <span class="keywordflow">if</span>(tau==Scalar(0)) <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;          tau = tau * m_qr.m_hcoeffs(k);</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;          res.col(j) -= tau * m_qr.m_Q.col(k);</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;        }</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;      }</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;    }</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;    {</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;      eigen_assert(m_qr.matrixQ().cols() == m_other.rows() &amp;&amp; <span class="stringliteral">&quot;Non conforming object sizes&quot;</span>);</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160; </div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;      res.conservativeResize(rows(), cols());</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160; </div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;      <span class="comment">// Compute res = Q * other column by column</span></div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; res.cols(); j++)</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;      {</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> start_k = internal::is_identity&lt;Derived&gt;::value ? numext::mini(j,diagSize-1) : diagSize-1;</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;        <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = start_k; k &gt;=0; k--)</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;        {</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;          Scalar tau = Scalar(0);</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;          tau = m_qr.m_Q.col(k).dot(res.col(j));</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;          <span class="keywordflow">if</span>(tau==Scalar(0)) <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;          tau = tau * numext::conj(m_qr.m_hcoeffs(k));</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;          res.col(j) -= tau * m_qr.m_Q.col(k);</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;        }</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;      }</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;    }</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;  }</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;  </div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;  <span class="keyword">const</span> SparseQRType&amp; m_qr;</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;  <span class="keyword">const</span> Derived&amp; m_other;</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;  <span class="keywordtype">bool</span> m_transpose; <span class="comment">// TODO this actually means adjoint</span></div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;};</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160; </div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SparseQRType&gt;</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;<span class="keyword">struct </span>SparseQRMatrixQReturnType : <span class="keyword">public</span> EigenBase&lt;SparseQRMatrixQReturnType&lt;SparseQRType&gt; &gt;</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;{  </div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::Scalar Scalar;</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar,Dynamic,Dynamic&gt; DenseMatrix;</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;    RowsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>,</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;    ColsAtCompileTime = <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a></div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;  };</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;  <span class="keyword">explicit</span> SparseQRMatrixQReturnType(<span class="keyword">const</span> SparseQRType&amp; qr) : m_qr(qr) {}</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;  SparseQR_QProduct&lt;SparseQRType, Derived&gt; <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator*</a>(<span class="keyword">const</span> MatrixBase&lt;Derived&gt;&amp; other)</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;  {</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;    <span class="keywordflow">return</span> SparseQR_QProduct&lt;SparseQRType,Derived&gt;(m_qr,other.derived(),<span class="keyword">false</span>);</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;  }</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;  <span class="comment">// To use for operations with the adjoint of Q</span></div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;  SparseQRMatrixQTransposeReturnType&lt;SparseQRType&gt; adjoint()<span class="keyword"> const</span></div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;    <span class="keywordflow">return</span> SparseQRMatrixQTransposeReturnType&lt;SparseQRType&gt;(m_qr);</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;  }</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;  <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;  <span class="keyword">inline</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;  <span class="comment">// To use for operations with the transpose of Q FIXME this is the same as adjoint at the moment</span></div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;  SparseQRMatrixQTransposeReturnType&lt;SparseQRType&gt; transpose()<span class="keyword"> const</span></div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;    <span class="keywordflow">return</span> SparseQRMatrixQTransposeReturnType&lt;SparseQRType&gt;(m_qr);</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;  }</div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  <span class="keyword">const</span> SparseQRType&amp; m_qr;</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;};</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160; </div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;<span class="comment">// TODO this actually represents the adjoint of Q</span></div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SparseQRType&gt;</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;<span class="keyword">struct </span>SparseQRMatrixQTransposeReturnType</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;{</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;  <span class="keyword">explicit</span> SparseQRMatrixQTransposeReturnType(<span class="keyword">const</span> SparseQRType&amp; qr) : m_qr(qr) {}</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;  SparseQR_QProduct&lt;SparseQRType,Derived&gt; <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator*</a>(<span class="keyword">const</span> MatrixBase&lt;Derived&gt;&amp; other)</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;  {</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;    <span class="keywordflow">return</span> SparseQR_QProduct&lt;SparseQRType,Derived&gt;(m_qr,other.derived(), <span class="keyword">true</span>);</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;  }</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;  <span class="keyword">const</span> SparseQRType&amp; m_qr;</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;};</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160; </div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;  </div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SparseQRType&gt;</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;<span class="keyword">struct </span>evaluator_traits&lt;SparseQRMatrixQReturnType&lt;SparseQRType&gt; &gt;</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;{</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::MatrixType MatrixType;</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> storage_kind_to_evaluator_kind&lt;typename MatrixType::StorageKind&gt;::Kind Kind;</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;  <span class="keyword">typedef</span> SparseShape Shape;</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;};</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160; </div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;<span class="keyword">template</span>&lt; <span class="keyword">typename</span> DstXprType, <span class="keyword">typename</span> SparseQRType&gt;</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;<span class="keyword">struct </span>Assignment&lt;DstXprType, SparseQRMatrixQReturnType&lt;SparseQRType&gt;, internal::assign_op&lt;typename DstXprType::Scalar,typename DstXprType::Scalar&gt;, Sparse2Sparse&gt;</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;{</div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;  <span class="keyword">typedef</span> SparseQRMatrixQReturnType&lt;SparseQRType&gt; SrcXprType;</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> DstXprType::Scalar Scalar;</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> DstXprType::StorageIndex StorageIndex;</div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(DstXprType &amp;dst, <span class="keyword">const</span> SrcXprType &amp;src, <span class="keyword">const</span> internal::assign_op&lt;Scalar,Scalar&gt; &amp;<span class="comment">/*func*/</span>)</div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;  {</div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;    <span class="keyword">typename</span> DstXprType::PlainObject idMat(src.rows(), src.cols());</div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;    idMat.setIdentity();</div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;    <span class="comment">// Sort the sparse householder reflectors if needed</span></div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;    <span class="keyword">const_cast&lt;</span>SparseQRType *<span class="keyword">&gt;</span>(&amp;src.m_qr)-&gt;_sort_matrix_Q();</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;    dst = SparseQR_QProduct&lt;SparseQRType, DstXprType&gt;(src.m_qr, idMat, <span class="keyword">false</span>);</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;  }</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;};</div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160; </div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;<span class="keyword">template</span>&lt; <span class="keyword">typename</span> DstXprType, <span class="keyword">typename</span> SparseQRType&gt;</div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;<span class="keyword">struct </span>Assignment&lt;DstXprType, SparseQRMatrixQReturnType&lt;SparseQRType&gt;, internal::assign_op&lt;typename DstXprType::Scalar,typename DstXprType::Scalar&gt;, Sparse2Dense&gt;</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;{</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;  <span class="keyword">typedef</span> SparseQRMatrixQReturnType&lt;SparseQRType&gt; SrcXprType;</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> DstXprType::Scalar Scalar;</div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> DstXprType::StorageIndex StorageIndex;</div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(DstXprType &amp;dst, <span class="keyword">const</span> SrcXprType &amp;src, <span class="keyword">const</span> internal::assign_op&lt;Scalar,Scalar&gt; &amp;<span class="comment">/*func*/</span>)</div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;  {</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;    dst = src.m_qr.matrixQ() * DstXprType::Identity(src.m_qr.rows(), src.m_qr.rows());</div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;  }</div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;};</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160; </div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160; </div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160; </div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::DenseCoeffsBase&lt; Derived, DirectWriteAccessors &gt;::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::DenseCoeffsBase&lt; Derived, DirectWriteAccessors &gt;::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix&lt; StorageIndex, Dynamic, 1 &gt;</a></div></div>
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<div class="ttc" id="aclassEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix&lt; Dynamic, Dynamic, StorageIndex &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_aac6bc5261783ec3008a51c2654de73e8"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#aac6bc5261783ec3008a51c2654de73e8">Eigen::PlainObjectBase::setConstant</a></div><div class="ttdeci">Derived &amp; setConstant(Index size, const Scalar &amp;val)</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:363</div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_ac54123f62de4c46a9107ff53890b6116"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#ac54123f62de4c46a9107ff53890b6116">Eigen::PlainObjectBase::data</a></div><div class="ttdeci">const Scalar * data() const</div><div class="ttdef"><b>Definition:</b> PlainObjectBase.h:259</div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_acc39eaf7ba22b725c86f1b9b8bb57c3c"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#acc39eaf7ba22b725c86f1b9b8bb57c3c">Eigen::PlainObjectBase::setZero</a></div><div class="ttdeci">Derived &amp; setZero(Index size)</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:564</div></div>
<div class="ttc" id="aclassEigen_1_1Solve_html"><div class="ttname"><a href="classEigen_1_1Solve.html">Eigen::Solve</a></div><div class="ttdoc">Pseudo expression representing a solving operation.</div><div class="ttdef"><b>Definition:</b> Solve.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrixBase_html"><div class="ttname"><a href="classEigen_1_1SparseMatrixBase.html">Eigen::SparseMatrixBase</a></div><div class="ttdoc">Base class of any sparse matrices or sparse expressions.</div><div class="ttdef"><b>Definition:</b> SparseMatrixBase.h:30</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrixBase_html_a1944e9fa9ce7937bfc3a87b2cb94371f"><div class="ttname"><a href="classEigen_1_1SparseMatrixBase.html#a1944e9fa9ce7937bfc3a87b2cb94371f">Eigen::SparseMatrixBase::rows</a></div><div class="ttdeci">Index rows() const</div><div class="ttdef"><b>Definition:</b> SparseMatrixBase.h:176</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html">Eigen::SparseMatrix&lt; Scalar, ColMajor, StorageIndex &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html_a36b8cc95234b4e2de38a199b6b2af9fc"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#a36b8cc95234b4e2de38a199b6b2af9fc">Eigen::SparseMatrix::cols</a></div><div class="ttdeci">Index cols() const</div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:142</div></div>
<div class="ttc" id="aclassEigen_1_1SparseMatrix_html_a853a76dd42349fa2f3654a4a61e0f574"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#a853a76dd42349fa2f3654a4a61e0f574">Eigen::SparseMatrix::rows</a></div><div class="ttdeci">Index rows() const</div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:140</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html"><div class="ttname"><a href="classEigen_1_1SparseQR.html">Eigen::SparseQR</a></div><div class="ttdoc">Sparse left-looking QR factorization with numerical column pivoting.</div><div class="ttdef"><b>Definition:</b> SparseQR.h:87</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_a05f11a211307cb106e9e47ee9730d7ed"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a05f11a211307cb106e9e47ee9730d7ed">Eigen::SparseQR::setPivotThreshold</a></div><div class="ttdeci">void setPivotThreshold(const RealScalar &amp;threshold)</div><div class="ttdef"><b>Definition:</b> SparseQR.h:237</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_a4b425ddb1358c914d764cde48853a4f6"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a4b425ddb1358c914d764cde48853a4f6">Eigen::SparseQR::analyzePattern</a></div><div class="ttdeci">void analyzePattern(const MatrixType &amp;mat)</div><div class="ttdoc">Preprocessing step of a QR factorization.</div><div class="ttdef"><b>Definition:</b> SparseQR.h:322</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_a55a34bacf05bd30a1dacbccad9f03c6d"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a55a34bacf05bd30a1dacbccad9f03c6d">Eigen::SparseQR::factorize</a></div><div class="ttdeci">void factorize(const MatrixType &amp;mat)</div><div class="ttdoc">Performs the numerical QR factorization of the input matrix.</div><div class="ttdef"><b>Definition:</b> SparseQR.h:363</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_a5f13e65437ada7e10a85de8cd55db11d"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a5f13e65437ada7e10a85de8cd55db11d">Eigen::SparseQR::SparseQR</a></div><div class="ttdeci">SparseQR(const MatrixType &amp;mat)</div><div class="ttdef"><b>Definition:</b> SparseQR.h:118</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_a6fdb992f3381ecc5b0a21a692fc0e0a4"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a6fdb992f3381ecc5b0a21a692fc0e0a4">Eigen::SparseQR::cols</a></div><div class="ttdeci">Index cols() const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:143</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_a7764a1f00c0d83f6423f81a4a40d5f8c"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a7764a1f00c0d83f6423f81a4a40d5f8c">Eigen::SparseQR::matrixR</a></div><div class="ttdeci">const QRMatrixType &amp; matrixR() const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:158</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_a9b196c075fdf32737b6843a615e79ea6"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a9b196c075fdf32737b6843a615e79ea6">Eigen::SparseQR::rows</a></div><div class="ttdeci">Index rows() const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:139</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_aa27f024fe063684754047c531ab84a2b"><div class="ttname"><a href="classEigen_1_1SparseQR.html#aa27f024fe063684754047c531ab84a2b">Eigen::SparseQR::colsPermutation</a></div><div class="ttdeci">const PermutationType &amp; colsPermutation() const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:194</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_aa3c7967f81ef047891a549a514908cd3"><div class="ttname"><a href="classEigen_1_1SparseQR.html#aa3c7967f81ef047891a549a514908cd3">Eigen::SparseQR::matrixQ</a></div><div class="ttdeci">SparseQRMatrixQReturnType&lt; SparseQR &gt; matrixQ() const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:188</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_aa77f5cb833bbea615adb532139761971"><div class="ttname"><a href="classEigen_1_1SparseQR.html#aa77f5cb833bbea615adb532139761971">Eigen::SparseQR::solve</a></div><div class="ttdeci">const Solve&lt; SparseQR, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;B) const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:248</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_ab9cc9c9d14e8c2f7587ca3f747bd1c14"><div class="ttname"><a href="classEigen_1_1SparseQR.html#ab9cc9c9d14e8c2f7587ca3f747bd1c14">Eigen::SparseQR::lastErrorMessage</a></div><div class="ttdeci">std::string lastErrorMessage() const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:203</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_aba8ae81fd3d4ce9139eccb6b7a0256b2"><div class="ttname"><a href="classEigen_1_1SparseQR.html#aba8ae81fd3d4ce9139eccb6b7a0256b2">Eigen::SparseQR::compute</a></div><div class="ttdeci">void compute(const MatrixType &amp;mat)</div><div class="ttdef"><b>Definition:</b> SparseQR.h:129</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_ae9da700b8c3b9bb30ff77508c359e764"><div class="ttname"><a href="classEigen_1_1SparseQR.html#ae9da700b8c3b9bb30ff77508c359e764">Eigen::SparseQR::info</a></div><div class="ttdeci">ComputationInfo info() const</div><div class="ttdoc">Reports whether previous computation was successful.</div><div class="ttdef"><b>Definition:</b> SparseQR.h:270</div></div>
<div class="ttc" id="aclassEigen_1_1SparseQR_html_afa0359921bffa067601b102edff440b0"><div class="ttname"><a href="classEigen_1_1SparseQR.html#afa0359921bffa067601b102edff440b0">Eigen::SparseQR::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition:</b> SparseQR.h:164</div></div>
<div class="ttc" id="aclassEigen_1_1SparseSolverBase_html"><div class="ttname"><a href="classEigen_1_1SparseSolverBase.html">Eigen::SparseSolverBase</a></div><div class="ttdoc">A base class for sparse solvers.</div><div class="ttdef"><b>Definition:</b> SparseSolverBase.h:70</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:442</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf">Eigen::InvalidInput</a></div><div class="ttdeci">@ InvalidInput</div><div class="ttdef"><b>Definition:</b> Constants.h:451</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_a9723b3ff0f2c99fe1081e3eb14380d4c"><div class="ttname"><a href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">Eigen::operator*</a></div><div class="ttdeci">const Product&lt; MatrixDerived, PermutationDerived, AliasFreeProduct &gt; operator*(const MatrixBase&lt; MatrixDerived &gt; &amp;matrix, const PermutationBase&lt; PermutationDerived &gt; &amp;permutation)</div><div class="ttdef"><b>Definition:</b> PermutationMatrix.h:517</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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